// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This code initially comes from MINPACK whose original authors are:
// Copyright Jorge More - Argonne National Laboratory
// Copyright Burt Garbow - Argonne National Laboratory
// Copyright Ken Hillstrom - Argonne National Laboratory
//
// This Source Code Form is subject to the terms of the Minpack license
// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.

#ifndef EIGEN_LMPAR_H
#define EIGEN_LMPAR_H

namespace Eigen {

namespace internal {

    template <typename QRSolver, typename VectorType>
    void lmpar2(const QRSolver& qr,
                const VectorType& diag,
                const VectorType& qtb,
                typename VectorType::Scalar m_delta,
                typename VectorType::Scalar& par,
                VectorType& x)

    {
        using std::abs;
        using std::sqrt;
        typedef typename QRSolver::MatrixType MatrixType;
        typedef typename QRSolver::Scalar Scalar;
        //    typedef typename QRSolver::StorageIndex StorageIndex;

        /* Local variables */
        Index j;
        Scalar fp;
        Scalar parc, parl;
        Index iter;
        Scalar temp, paru;
        Scalar gnorm;
        Scalar dxnorm;

        // Make a copy of the triangular factor.
        // This copy is modified during call the qrsolv
        MatrixType s;
        s = qr.matrixR();

        /* Function Body */
        const Scalar dwarf = (std::numeric_limits<Scalar>::min)();
        const Index n = qr.matrixR().cols();
        eigen_assert(n == diag.size());
        eigen_assert(n == qtb.size());

        VectorType wa1, wa2;

        /* compute and store in x the gauss-newton direction. if the */
        /* jacobian is rank-deficient, obtain a least squares solution. */

        //    const Index rank = qr.nonzeroPivots(); // exactly double(0.)
        const Index rank = qr.rank();  // use a threshold
        wa1 = qtb;
        wa1.tail(n - rank).setZero();
        //FIXME There is no solve in place for sparse triangularView
        wa1.head(rank) = s.topLeftCorner(rank, rank).template triangularView<Upper>().solve(qtb.head(rank));

        x = qr.colsPermutation() * wa1;

        /* initialize the iteration counter. */
        /* evaluate the function at the origin, and test */
        /* for acceptance of the gauss-newton direction. */
        iter = 0;
        wa2 = diag.cwiseProduct(x);
        dxnorm = wa2.blueNorm();
        fp = dxnorm - m_delta;
        if (fp <= Scalar(0.1) * m_delta)
        {
            par = 0;
            return;
        }

        /* if the jacobian is not rank deficient, the newton */
        /* step provides a lower bound, parl, for the zero of */
        /* the function. otherwise set this bound to zero. */
        parl = 0.;
        if (rank == n)
        {
            wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2) / dxnorm;
            s.topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1);
            temp = wa1.blueNorm();
            parl = fp / m_delta / temp / temp;
        }

        /* calculate an upper bound, paru, for the zero of the function. */
        for (j = 0; j < n; ++j) wa1[j] = s.col(j).head(j + 1).dot(qtb.head(j + 1)) / diag[qr.colsPermutation().indices()(j)];

        gnorm = wa1.stableNorm();
        paru = gnorm / m_delta;
        if (paru == 0.)
            paru = dwarf / (std::min)(m_delta, Scalar(0.1));

        /* if the input par lies outside of the interval (parl,paru), */
        /* set par to the closer endpoint. */
        par = (std::max)(par, parl);
        par = (std::min)(par, paru);
        if (par == 0.)
            par = gnorm / dxnorm;

        /* beginning of an iteration. */
        while (true)
        {
            ++iter;

            /* evaluate the function at the current value of par. */
            if (par == 0.)
                par = (std::max)(dwarf, Scalar(.001) * paru); /* Computing MAX */
            wa1 = sqrt(par) * diag;

            VectorType sdiag(n);
            lmqrsolv(s, qr.colsPermutation(), wa1, qtb, x, sdiag);

            wa2 = diag.cwiseProduct(x);
            dxnorm = wa2.blueNorm();
            temp = fp;
            fp = dxnorm - m_delta;

            /* if the function is small enough, accept the current value */
            /* of par. also test for the exceptional cases where parl */
            /* is zero or the number of iterations has reached 10. */
            if (abs(fp) <= Scalar(0.1) * m_delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
                break;

            /* compute the newton correction. */
            wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2 / dxnorm);
            // we could almost use this here, but the diagonal is outside qr, in sdiag[]
            for (j = 0; j < n; ++j)
            {
                wa1[j] /= sdiag[j];
                temp = wa1[j];
                for (Index i = j + 1; i < n; ++i) wa1[i] -= s.coeff(i, j) * temp;
            }
            temp = wa1.blueNorm();
            parc = fp / m_delta / temp / temp;

            /* depending on the sign of the function, update parl or paru. */
            if (fp > 0.)
                parl = (std::max)(parl, par);
            if (fp < 0.)
                paru = (std::min)(paru, par);

            /* compute an improved estimate for par. */
            par = (std::max)(parl, par + parc);
        }
        if (iter == 0)
            par = 0.;
        return;
    }
}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_LMPAR_H
